I need two methods different conclusion. \(\displaystyle\lim_{{{\left({x},{y}\right)}\to{\left({0},{0}\right)}}}{\frac{{{\left({x}^{{3}}-{y}^{{2}}\right)}^{{2}}}}{{{x}^{{4}}+{y}^{{4}}}}}\)

Jasiah Vincent

Jasiah Vincent

Answered question

2022-04-07

I need two methods different conclusion.
lim(x,y)(0,0)(x3y2)2x4+y4

Answer & Explanation

entreblogsmc2j

entreblogsmc2j

Beginner2022-04-08Added 10 answers

This can be done simply:
Take a path with x=0 and y0; then (x3-y2)2x4+y4=y4y4=1
Take a path with y=0 and x0; then (x3y2)2x4+y4=x6x4=x20
So lim(x,y)(0,0)(x3y2)2x4+y4 does not exist.

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